Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [752,4,Mod(1,752)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(752, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("752.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 752 = 2^{4} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 752.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(44.3694363243\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 47) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.68740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 752.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.777884 | 0.149704 | 0.0748519 | − | 0.997195i | \(-0.476152\pi\) | ||||
0.0748519 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.19383 | 0.822321 | 0.411161 | − | 0.911563i | \(-0.365124\pi\) | ||||
0.411161 | + | 0.911563i | \(0.365124\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.3255 | 1.63742 | 0.818711 | − | 0.574206i | \(-0.194689\pi\) | ||||
0.818711 | + | 0.574206i | \(0.194689\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.3949 | −0.977589 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.4298 | −0.614803 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.0257 | −1.32330 | −0.661648 | − | 0.749815i | \(-0.730143\pi\) | ||||
−0.661648 | + | 0.749815i | \(0.730143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.15173 | 0.123105 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −72.1639 | −1.02955 | −0.514774 | − | 0.857326i | \(-0.672124\pi\) | ||||
−0.514774 | + | 0.857326i | \(0.672124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.0550 | 0.302526 | 0.151263 | − | 0.988494i | \(-0.451666\pi\) | ||||
0.151263 | + | 0.988494i | \(0.451666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23.5897 | 0.245128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −103.176 | −0.935373 | −0.467687 | − | 0.883894i | \(-0.654912\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −40.4735 | −0.323788 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −41.5350 | −0.296052 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −234.381 | −1.50081 | −0.750405 | − | 0.660978i | \(-0.770142\pi\) | ||||
−0.750405 | + | 0.660978i | \(0.770142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −198.714 | −1.15129 | −0.575647 | − | 0.817698i | \(-0.695250\pi\) | ||||
−0.575647 | + | 0.817698i | \(0.695250\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.4477 | −0.0920383 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 278.807 | 1.34649 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −203.083 | −0.902343 | −0.451171 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451171 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −48.2488 | −0.198102 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.889 | 0.803303 | 0.401651 | − | 0.915793i | \(-0.368436\pi\) | ||||
0.401651 | + | 0.915793i | \(0.368436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −111.430 | −0.395184 | −0.197592 | − | 0.980284i | \(-0.563312\pi\) | ||||
−0.197592 | + | 0.980284i | \(0.563312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −242.670 | −0.803892 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −47.0000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 576.634 | 1.68115 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −56.1351 | −0.154127 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 499.576 | 1.29476 | 0.647378 | − | 0.762169i | \(-0.275866\pi\) | ||||
0.647378 | + | 0.762169i | \(0.275866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −206.215 | −0.505565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.4898 | 0.0452894 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 562.752 | 1.24176 | 0.620882 | − | 0.783904i | \(-0.286775\pi\) | ||||
0.620882 | + | 0.783904i | \(0.286775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 548.091 | 1.15042 | 0.575212 | − | 0.818004i | \(-0.304919\pi\) | ||||
0.575212 | + | 0.818004i | \(0.304919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −800.437 | −1.60072 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −570.254 | −1.08817 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 760.831 | 1.38732 | 0.693659 | − | 0.720304i | \(-0.255998\pi\) | ||||
0.693659 | + | 0.720304i | \(0.255998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −80.2586 | −0.140029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 668.059 | 1.11668 | 0.558338 | − | 0.829613i | \(-0.311439\pi\) | ||||
0.558338 | + | 0.829613i | \(0.311439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1145.92 | −1.83726 | −0.918629 | − | 0.395121i | \(-0.870703\pi\) | ||||
−0.918629 | + | 0.395121i | \(0.870703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −31.4836 | −0.0484722 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −680.193 | −1.00669 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −975.010 | −1.38857 | −0.694286 | − | 0.719699i | \(-0.744280\pi\) | ||||
−0.694286 | + | 0.719699i | \(0.744280\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 680.353 | 0.933269 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −698.827 | −0.924171 | −0.462086 | − | 0.886835i | \(-0.652899\pi\) | ||||
−0.462086 | + | 0.886835i | \(0.652899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −663.463 | −0.846620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −182.321 | −0.224677 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 451.477 | 0.537713 | 0.268857 | − | 0.963180i | \(-0.413354\pi\) | ||||
0.268857 | + | 0.963180i | \(0.413354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1880.96 | −2.16679 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −154.577 | −0.172353 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 230.351 | 0.248774 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −390.906 | −0.409180 | −0.204590 | − | 0.978848i | \(-0.565586\pi\) | ||||
−0.204590 | + | 0.978848i | \(0.565586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 592.031 | 0.601024 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1112.66 | −1.09618 | −0.548089 | − | 0.836420i | \(-0.684644\pi\) | ||||
−0.548089 | + | 0.836420i | \(0.684644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 882.574 | 0.844298 | 0.422149 | − | 0.906527i | \(-0.361276\pi\) | ||||
0.422149 | + | 0.906527i | \(0.361276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 216.880 | 0.201574 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −840.742 | −0.759604 | −0.379802 | − | 0.925068i | \(-0.624008\pi\) | ||||
−0.379802 | + | 0.925068i | \(0.624008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1321.06 | −1.16086 | −0.580432 | − | 0.814309i | \(-0.697116\pi\) | ||||
−0.580432 | + | 0.814309i | \(0.697116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −157.975 | −0.135084 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 701.293 | 0.583824 | 0.291912 | − | 0.956445i | \(-0.405709\pi\) | ||||
0.291912 | + | 0.956445i | \(0.405709\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −948.579 | −0.769177 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1637.16 | 1.29364 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2188.40 | −1.68580 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −827.906 | −0.622018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 164.047 | 0.120257 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.34 | −1.08858 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1142.65 | −0.798374 | −0.399187 | − | 0.916869i | \(-0.630708\pi\) | ||||
−0.399187 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −86.6795 | −0.0591605 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −104.451 | −0.0696639 | −0.0348319 | − | 0.999393i | \(-0.511090\pi\) | ||||
−0.0348319 | + | 0.999393i | \(0.511090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 759.803 | 0.495363 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −381.866 | −0.243450 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −543.914 | −0.339195 | −0.169598 | − | 0.985513i | \(-0.554247\pi\) | ||||
−0.169598 | + | 0.985513i | \(0.554247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 41.8374 | 0.0255295 | 0.0127647 | − | 0.999919i | \(-0.495937\pi\) | ||||
0.0127647 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −36.5605 | −0.0218365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1391.22 | 0.813565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2154.86 | −1.23415 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 448.554 | 0.251674 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 790.139 | 0.434435 | 0.217217 | − | 0.976123i | \(-0.430302\pi\) | ||||
0.217217 | + | 0.976123i | \(0.430302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2073.79 | 1.11763 | 0.558816 | − | 0.829292i | \(-0.311256\pi\) | ||||
0.558816 | + | 0.829292i | \(0.311256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1904.76 | 1.00648 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1826.95 | −0.946734 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2501.12 | 1.27141 | 0.635704 | − | 0.771933i | \(-0.280710\pi\) | ||||
0.635704 | + | 0.771933i | \(0.280710\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 388.612 | 0.193830 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3128.85 | −1.53160 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 97.0569 | 0.0466386 | 0.0233193 | − | 0.999728i | \(-0.492577\pi\) | ||||
0.0233193 | + | 0.999728i | \(0.492577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −160.412 | −0.0756850 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1826.71 | 0.846437 | 0.423218 | − | 0.906028i | \(-0.360900\pi\) | ||||
0.423218 | + | 0.906028i | \(0.360900\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1650.19 | 0.751111 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −661.323 | −0.295746 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1843.63 | −0.810223 | −0.405111 | − | 0.914267i | \(-0.632767\pi\) | ||||
−0.405111 | + | 0.914267i | \(0.632767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1227.38 | −0.530177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 437.756 | 0.185897 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 370.515 | 0.154713 | 0.0773565 | − | 0.997003i | \(-0.475352\pi\) | ||||
0.0773565 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −866.586 | −0.355872 | −0.177936 | − | 0.984042i | \(-0.556942\pi\) | ||||
−0.177936 | + | 0.984042i | \(0.556942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 426.351 | 0.172223 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1867.11 | −0.742016 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1618.62 | 0.632969 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1259.57 | −0.484763 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3667.49 | 1.38937 | 0.694687 | − | 0.719312i | \(-0.255543\pi\) | ||||
0.694687 | + | 0.719312i | \(0.255543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4676.91 | −1.74431 | −0.872154 | − | 0.489231i | \(-0.837277\pi\) | ||||
−0.872154 | + | 0.489231i | \(0.837277\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −443.591 | −0.162904 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3700.99 | 1.33850 | 0.669251 | − | 0.743037i | \(-0.266615\pi\) | ||||
0.669251 | + | 0.743037i | \(0.266615\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1361.63 | 0.485042 | 0.242521 | − | 0.970146i | \(-0.422026\pi\) | ||||
0.242521 | + | 0.970146i | \(0.422026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 591.838 | 0.207687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7107.72 | −2.45746 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1938.88 | 0.660573 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2723.31 | 0.914411 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −561.977 | −0.185994 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2873.21 | 0.937442 | 0.468721 | − | 0.883346i | \(-0.344715\pi\) | ||||
0.468721 | + | 0.883346i | \(0.344715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 519.672 | 0.167171 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1024.47 | −0.324968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6026.10 | −1.88515 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −891.393 | −0.275044 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4476.02 | 1.36240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3356.14 | −1.00782 | −0.503909 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503909 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1068.29 | 0.316531 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3991.01 | 1.16693 | 0.583464 | − | 0.812139i | \(-0.301697\pi\) | ||||
0.583464 | + | 0.812139i | \(0.301697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −968.028 | −0.279341 | −0.139670 | − | 0.990198i | \(-0.544604\pi\) | ||||
−0.139670 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −529.111 | −0.150705 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1227.70 | −0.345189 | −0.172595 | − | 0.984993i | \(-0.555215\pi\) | ||||
−0.172595 | + | 0.984993i | \(0.555215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −432.110 | −0.119948 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −758.444 | −0.207875 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −647.534 | −0.175253 | −0.0876265 | − | 0.996153i | \(-0.527928\pi\) | ||||
−0.0876265 | + | 0.996153i | \(0.527928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4174.42 | −1.11576 | −0.557880 | − | 0.829922i | \(-0.688385\pi\) | ||||
−0.557880 | + | 0.829922i | \(0.688385\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1650.68 | 0.435766 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5301.47 | 1.38244 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1554.05 | −0.400332 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −543.606 | −0.138352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1368.39 | 0.344112 | 0.172056 | − | 0.985087i | \(-0.444959\pi\) | ||||
0.172056 | + | 0.985087i | \(0.444959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2314.20 | 0.575070 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −516.097 | −0.126742 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1709.94 | 0.415031 | 0.207515 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207515 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6158.59 | −1.47752 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6186.47 | 1.46718 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5368.95 | −1.25880 | −0.629399 | − | 0.777082i | \(-0.716699\pi\) | ||||
−0.629399 | + | 0.777082i | \(0.716699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4593.02 | 1.06471 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 351.197 | 0.0804977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4213.70 | −0.955070 | −0.477535 | − | 0.878613i | \(-0.658470\pi\) | ||||
−0.477535 | + | 0.878613i | \(0.658470\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4769.83 | −1.06918 | −0.534588 | − | 0.845113i | \(-0.679533\pi\) | ||||
−0.534588 | + | 0.845113i | \(0.679533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1463.17 | −0.324377 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 907.810 | 0.199066 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5651.38 | 1.22584 | 0.612922 | − | 0.790144i | \(-0.289994\pi\) | ||||
0.612922 | + | 0.790144i | \(0.289994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5245.04 | 1.12549 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3264.83 | 0.693109 | 0.346554 | − | 0.938030i | \(-0.387352\pi\) | ||||
0.346554 | + | 0.938030i | \(0.387352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2019.38 | −0.424169 | −0.212084 | − | 0.977251i | \(-0.568025\pi\) | ||||
−0.212084 | + | 0.977251i | \(0.568025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 179.186 | 0.0372424 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6395.32 | 1.31534 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 294.634 | 0.0599703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −304.079 | −0.0612558 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3432.28 | 0.684354 | 0.342177 | − | 0.939636i | \(-0.388836\pi\) | ||||
0.342177 | + | 0.939636i | \(0.388836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5173.85 | 1.02113 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 931.621 | 0.182014 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6399.54 | 1.23778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3379.16 | −0.647082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −865.521 | −0.164102 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5039.06 | 0.946019 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6327.92 | 1.17640 | 0.588198 | − | 0.808717i | \(-0.299838\pi\) | ||||
0.588198 | + | 0.808717i | \(0.299838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 686.540 | 0.126395 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9118.69 | −1.66262 | −0.831308 | − | 0.555812i | \(-0.812408\pi\) | ||||
−0.831308 | + | 0.555812i | \(0.812408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4611.70 | 0.832808 | 0.416404 | − | 0.909180i | \(-0.363290\pi\) | ||||
0.416404 | + | 0.909180i | \(0.363290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7359.09 | −1.31631 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4243.78 | −0.751907 | −0.375954 | − | 0.926638i | \(-0.622685\pi\) | ||||
−0.375954 | + | 0.926638i | \(0.622685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5257.12 | 0.922702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −654.000 | −0.113716 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1808.06 | −0.311466 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2510.40 | 0.428467 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1027.63 | −0.173786 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1425.30 | −0.238842 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3803.59 | 0.631613 | 0.315807 | − | 0.948824i | \(-0.397725\pi\) | ||||
0.315807 | + | 0.948824i | \(0.397725\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5360.36 | 0.882120 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6994.95 | 1.14082 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6419.12 | −1.03760 | −0.518801 | − | 0.854895i | \(-0.673621\pi\) | ||||
−0.518801 | + | 0.854895i | \(0.673621\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 545.524 | 0.0874006 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4457.11 | 0.707819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7085.05 | 1.11533 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −737.884 | −0.115149 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3495.57 | 0.540783 | 0.270392 | − | 0.962750i | \(-0.412847\pi\) | ||||
0.270392 | + | 0.962750i | \(0.412847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −435.838 | −0.0668477 | −0.0334239 | − | 0.999441i | \(-0.510641\pi\) | ||||
−0.0334239 | + | 0.999441i | \(0.510641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2576.24 | 0.391765 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1941.73 | 0.292771 | 0.146385 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146385 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6142.03 | 0.918267 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1702.32 | −0.252371 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7188.88 | −1.05687 | −0.528433 | − | 0.848975i | \(-0.677220\pi\) | ||||
−0.528433 | + | 0.848975i | \(0.677220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6231.25 | −0.908478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −644.014 | −0.0931184 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10535.4 | −1.51082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1674.78 | −0.238209 | −0.119105 | − | 0.992882i | \(-0.538002\pi\) | ||||
−0.119105 | + | 0.992882i | \(0.538002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5566.41 | −0.785300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15149.9 | 2.12006 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6028.31 | 0.836820 | 0.418410 | − | 0.908258i | \(-0.362588\pi\) | ||||
0.418410 | + | 0.908258i | \(0.362588\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1183.42 | −0.162964 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14537.7 | 1.98602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2065.63 | 0.279959 | 0.139979 | − | 0.990154i | \(-0.455296\pi\) | ||||
0.139979 | + | 0.990154i | \(0.455296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −888.846 | −0.119520 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7634.28 | −1.01852 | −0.509260 | − | 0.860613i | \(-0.670081\pi\) | ||||
−0.509260 | + | 0.860613i | \(0.670081\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6253.58 | −0.827823 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2941.18 | 0.386327 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2814.13 | −0.366792 | −0.183396 | − | 0.983039i | \(-0.558709\pi\) | ||||
−0.183396 | + | 0.983039i | \(0.558709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7445.55 | 0.963012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −81.2511 | −0.0104289 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8964.08 | −1.14185 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8990.52 | 1.13658 | 0.568288 | − | 0.822829i | \(-0.307606\pi\) | ||||
0.568288 | + | 0.822829i | \(0.307606\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 591.039 | 0.0741577 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4829.93 | −0.601484 | −0.300742 | − | 0.953706i | \(-0.597234\pi\) | ||||
−0.300742 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12325.4 | 1.52350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6255.05 | 0.767447 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4555.11 | 0.554763 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6551.78 | −0.792089 | −0.396045 | − | 0.918231i | \(-0.629617\pi\) | ||||
−0.396045 | + | 0.918231i | \(0.629617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −423.102 | −0.0507788 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17065.7 | 2.03329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6424.90 | −0.759966 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.5446 | 0.00382186 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10660.5 | −1.24296 | −0.621481 | − | 0.783429i | \(-0.713469\pi\) | ||||
−0.621481 | + | 0.783429i | \(0.713469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8654.47 | −1.00188 | −0.500942 | − | 0.865481i | \(-0.667013\pi\) | ||||
−0.500942 | + | 0.865481i | \(0.667013\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1240.56 | 0.142596 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2920.73 | 0.333355 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16621.1 | 1.88373 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1082.21 | 0.121794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4990.22 | −0.557703 | −0.278852 | − | 0.960334i | \(-0.589954\pi\) | ||||
−0.278852 | + | 0.960334i | \(0.589954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7921.49 | −0.879174 | −0.439587 | − | 0.898200i | \(-0.644875\pi\) | ||||
−0.439587 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1676.23 | −0.184757 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2585.06 | −0.282975 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11034.1 | −1.19961 | −0.599807 | − | 0.800145i | \(-0.704756\pi\) | ||||
−0.599807 | + | 0.800145i | \(0.704756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15220.2 | −1.64347 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9160.66 | −0.982474 | −0.491237 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491237 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4150.80 | 0.442173 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 614.636 | 0.0650365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10071.1 | −1.05854 | −0.529271 | − | 0.848453i | \(-0.677535\pi\) | ||||
−0.529271 | + | 0.848453i | \(0.677535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4730.20 | −0.493872 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1613.16 | 0.167314 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17293.2 | −1.78180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2988.54 | −0.305904 | −0.152952 | − | 0.988234i | \(-0.548878\pi\) | ||||
−0.152952 | + | 0.988234i | \(0.548878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2997.33 | 0.304800 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 956.638 | 0.0966487 | 0.0483244 | − | 0.998832i | \(-0.484612\pi\) | ||||
0.0483244 | + | 0.998832i | \(0.484612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4352.75 | 0.436910 | 0.218455 | − | 0.975847i | \(-0.429898\pi\) | ||||
0.218455 | + | 0.975847i | \(0.429898\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1421.15 | −0.141730 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8131.35 | −0.805725 | −0.402863 | − | 0.915260i | \(-0.631985\pi\) | ||||
−0.402863 | + | 0.915260i | \(0.631985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23072.5 | 2.27162 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1945.58 | 0.190335 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2499.35 | 0.242960 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1014.06 | −0.0979544 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13186.3 | −1.26574 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12912.4 | 1.23170 | 0.615849 | − | 0.787864i | \(-0.288813\pi\) | ||||
0.615849 | + | 0.787864i | \(0.288813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12596.4 | 1.19407 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2433.88 | −0.229286 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3593.92 | −0.336477 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11010.0 | 1.02446 | 0.512228 | − | 0.858850i | \(-0.328820\pi\) | ||||
0.512228 | + | 0.858850i | \(0.328820\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 75.4990 | 0.00698197 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14636.7 | 1.34531 | 0.672655 | − | 0.739956i | \(-0.265154\pi\) | ||||
0.672655 | + | 0.739956i | \(0.265154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16913.9 | 1.54516 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5443.04 | 0.494235 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20259.2 | 1.82847 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7549.78 | 0.677304 | 0.338652 | − | 0.940912i | \(-0.390029\pi\) | ||||
0.338652 | + | 0.940912i | \(0.390029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1420.97 | 0.126715 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16150.9 | 1.43167 | 0.715837 | − | 0.698267i | \(-0.246045\pi\) | ||||
0.715837 | + | 0.698267i | \(0.246045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10229.6 | −0.901410 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1283.66 | 0.112444 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19183.7 | 1.67053 | 0.835266 | − | 0.549846i | \(-0.185314\pi\) | ||||
0.835266 | + | 0.549846i | \(0.185314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34750.6 | −3.00836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1040.66 | −0.0895637 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8114.24 | 0.694284 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1054.20 | 0.0896782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1434.13 | −0.121293 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6867.69 | 0.577503 | 0.288751 | − | 0.957404i | \(-0.406760\pi\) | ||||
0.288751 | + | 0.957404i | \(0.406760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11205.2 | −0.936841 | −0.468420 | − | 0.883506i | \(-0.655177\pi\) | ||||
−0.468420 | + | 0.883506i | \(0.655177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −954.756 | −0.0793695 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14340.0 | 1.18531 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1521.81 | −0.125076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14853.8 | −1.21393 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13080.6 | −1.06301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7729.64 | −0.624639 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 288.218 | 0.0231611 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12933.8 | −1.03357 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14471.4 | 1.15004 | 0.575021 | − | 0.818139i | \(-0.304994\pi\) | ||||
0.575021 | + | 0.818139i | \(0.304994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −674.103 | −0.0532754 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12145.6 | −0.954603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13482.7 | 1.05389 | 0.526946 | − | 0.849899i | \(-0.323337\pi\) | ||||
0.526946 | + | 0.849899i | \(0.323337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14466.8 | −1.12464 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5872.41 | −0.454035 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29567.6 | −2.27368 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1452.40 | −0.111083 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10194.0 | 0.775466 | 0.387733 | − | 0.921772i | \(-0.373258\pi\) | ||||
0.387733 | + | 0.921772i | \(0.373258\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6911.52 | 0.522945 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1259.10 | 0.0947579 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3725.21 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6447.57 | 0.480091 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20632.0 | 1.52815 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6274.57 | −0.462291 | −0.231145 | − | 0.972919i | \(-0.574247\pi\) | ||||
−0.231145 | + | 0.972919i | \(0.574247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20390.6 | −1.49443 | −0.747214 | − | 0.664584i | \(-0.768609\pi\) | ||||
−0.747214 | + | 0.664584i | \(0.768609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2852.88 | 0.207995 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4175.87 | 0.302862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 675.385 | 0.0487290 | 0.0243645 | − | 0.999703i | \(-0.492244\pi\) | ||||
0.0243645 | + | 0.999703i | \(0.492244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3638.09 | −0.261130 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21192.3 | −1.51326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11205.4 | −0.796019 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15051.8 | 1.06379 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5949.63 | 0.418343 | 0.209172 | − | 0.977879i | \(-0.432923\pi\) | ||||
0.209172 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4978.78 | −0.348297 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2878.94 | 0.200379 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22071.9 | −1.52847 | −0.764235 | − | 0.644937i | \(-0.776883\pi\) | ||||
−0.764235 | + | 0.644937i | \(0.776883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20119.8 | −1.38627 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1059.19 | 0.0726126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9547.79 | 0.651272 | 0.325636 | − | 0.945495i | \(-0.394422\pi\) | ||||
0.325636 | + | 0.945495i | \(0.394422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12303.7 | −0.835076 | −0.417538 | − | 0.908660i | \(-0.637107\pi\) | ||||
−0.417538 | + | 0.908660i | \(0.637107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20082.0 | −1.35623 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7611.63 | −0.511498 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18252.2 | −1.22049 | −0.610243 | − | 0.792214i | \(-0.708928\pi\) | ||||
−0.610243 | + | 0.792214i | \(0.708928\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5528.98 | −0.367891 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2915.21 | 0.193022 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13990.5 | −0.921809 | −0.460905 | − | 0.887450i | \(-0.652475\pi\) | ||||
−0.460905 | + | 0.887450i | \(0.652475\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1508.22 | 0.0988902 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5747.16 | −0.374995 | −0.187498 | − | 0.982265i | \(-0.560038\pi\) | ||||
−0.187498 | + | 0.982265i | \(0.560038\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3913.70 | 0.254127 | 0.127064 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4285.40 | 0.276920 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13691.3 | 0.880463 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8927.71 | −0.571374 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −437.153 | −0.0278440 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14655.3 | 0.929006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26311.5 | −1.65998 | −0.829988 | − | 0.557781i | \(-0.811653\pi\) | ||||
−0.829988 | + | 0.557781i | \(0.811653\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2235.03 | 0.140339 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10505.3 | −0.656520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35766.1 | −2.22466 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17633.4 | −1.09165 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15538.7 | 0.957476 | 0.478738 | − | 0.877958i | \(-0.341094\pi\) | ||||
0.478738 | + | 0.877958i | \(0.341094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6125.10 | −0.375661 | −0.187831 | − | 0.982201i | \(-0.560146\pi\) | ||||
−0.187831 | + | 0.982201i | \(0.560146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −796.917 | −0.0486489 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4635.86 | −0.281692 | −0.140846 | − | 0.990032i | \(-0.544982\pi\) | ||||
−0.140846 | + | 0.990032i | \(0.544982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12622.4 | −0.763440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4687.61 | −0.282215 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11926.6 | −0.714740 | −0.357370 | − | 0.933963i | \(-0.616326\pi\) | ||||
−0.357370 | + | 0.933963i | \(0.616326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −960.309 | −0.0572861 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30246.4 | 1.79608 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −881.384 | −0.0520999 | −0.0260500 | − | 0.999661i | \(-0.508293\pi\) | ||||
−0.0260500 | + | 0.999661i | \(0.508293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19161.6 | −1.12753 | −0.563766 | − | 0.825935i | \(-0.690648\pi\) | ||||
−0.563766 | + | 0.825935i | \(0.690648\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3481.82 | 0.203956 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6985.50 | 0.407348 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24182.4 | 1.40382 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2610.68 | −0.150874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12293.6 | −0.707284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20156.0 | 1.15447 | 0.577235 | − | 0.816578i | \(-0.304132\pi\) | ||||
0.577235 | + | 0.816578i | \(0.304132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1681.07 | 0.0958582 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5567.34 | 0.316056 | 0.158028 | − | 0.987435i | \(-0.449486\pi\) | ||||
0.158028 | + | 0.987435i | \(0.449486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11854.4 | −0.670000 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3104.54 | 0.174694 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27835.8 | 1.55946 | 0.779728 | − | 0.626118i | \(-0.215357\pi\) | ||||
0.779728 | + | 0.626118i | \(0.215357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5000.66 | −0.278927 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −753.013 | −0.0418184 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30986.6 | −1.71334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17125.7 | −0.942824 | −0.471412 | − | 0.881913i | \(-0.656255\pi\) | ||||
−0.471412 | + | 0.881913i | \(0.656255\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17953.6 | 0.984129 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 384.646 | 0.0209934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15218.6 | −0.827039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −955.005 | −0.0516761 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5107.63 | 0.275196 | 0.137598 | − | 0.990488i | \(-0.456062\pi\) | ||||
0.137598 | + | 0.990488i | \(0.456062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5088.24 | −0.272983 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −336.131 | −0.0179566 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33742.0 | −1.79490 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11258.0 | 0.596335 | 0.298167 | − | 0.954514i | \(-0.403625\pi\) | ||||
0.298167 | + | 0.954514i | \(0.403625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25735.3 | 1.35745 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20502.5 | 1.07689 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12790.7 | 0.669012 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −503.706 | −0.0262360 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13735.6 | 0.712448 | 0.356224 | − | 0.934401i | \(-0.384064\pi\) | ||||
0.356224 | + | 0.934401i | \(0.384064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26764.5 | 1.38247 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3247.21 | −0.167033 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9486.22 | 0.485944 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14515.4 | −0.740502 | −0.370251 | − | 0.928932i | \(-0.620728\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17085.5 | −0.868033 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8041.22 | 0.406861 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14218.5 | 0.716471 | 0.358236 | − | 0.933631i | \(-0.383378\pi\) | ||||
0.358236 | + | 0.933631i | \(0.383378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4123.93 | 0.206957 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17065.3 | −0.852926 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8651.36 | −0.430643 | −0.215322 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215322 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1208.87 | −0.0599312 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37263.7 | 1.83993 | 0.919967 | − | 0.391996i | \(-0.128215\pi\) | ||||
0.919967 | + | 0.391996i | \(0.128215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7264.41 | 0.357245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18445.5 | 0.903460 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25495.9 | −1.24379 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33980.7 | 1.65110 | 0.825548 | − | 0.564331i | \(-0.190866\pi\) | ||||
0.825548 | + | 0.564331i | \(0.190866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1064.45 | 0.0515148 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19066.0 | 0.919052 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33247.9 | −1.59632 | −0.798161 | − | 0.602445i | \(-0.794193\pi\) | ||||
−0.798161 | + | 0.602445i | \(0.794193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1800.18 | 0.0860901 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13023.6 | −0.620376 | −0.310188 | − | 0.950675i | \(-0.600392\pi\) | ||||
−0.310188 | + | 0.950675i | \(0.600392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40061.6 | −1.90082 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17512.0 | 0.827646 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34905.1 | −1.64322 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26526.2 | 1.24390 | 0.621949 | − | 0.783057i | \(-0.286341\pi\) | ||||
0.621949 | + | 0.783057i | \(0.286341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1330.13 | 0.0621316 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1143.17 | 0.0531914 | 0.0265957 | − | 0.999646i | \(-0.491533\pi\) | ||||
0.0265957 | + | 0.999646i | \(0.491533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8042.65 | 0.372775 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4790.67 | −0.221190 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5283.83 | 0.243020 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14984.4 | −0.686536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9735.03 | 0.444319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22994.9 | 1.04551 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41354.8 | −1.87311 | −0.936556 | − | 0.350519i | \(-0.886005\pi\) | ||||
−0.936556 | + | 0.350519i | \(0.886005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4176.42 | −0.188447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21267.0 | 0.955965 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33995.8 | −1.52235 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3572.83 | 0.159390 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8795.77 | 0.390918 | 0.195459 | − | 0.980712i | \(-0.437380\pi\) | ||||
0.195459 | + | 0.980712i | \(0.437380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3391.71 | 0.150175 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11916.7 | −0.525662 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25702.7 | 1.12955 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28766.1 | −1.25947 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3277.77 | −0.142978 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2152.09 | 0.0935272 | 0.0467636 | − | 0.998906i | \(-0.485109\pi\) | ||||
0.0467636 | + | 0.998906i | \(0.485109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24307.1 | −1.05245 | −0.526225 | − | 0.850346i | \(-0.676393\pi\) | ||||
−0.526225 | + | 0.850346i | \(0.676393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3710.38 | −0.160060 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 892.325 | 0.0383519 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2791.87 | −0.119554 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 49647.7 | 2.11823 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45118.9 | 1.91798 | 0.958988 | − | 0.283446i | \(-0.0914775\pi\) | ||||
0.958988 | + | 0.283446i | \(0.0914775\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38608.9 | −1.63526 | −0.817631 | − | 0.575742i | \(-0.804713\pi\) | ||||
−0.817631 | + | 0.575742i | \(0.804713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 706.171 | 0.0298009 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17908.8 | 0.753023 | 0.376512 | − | 0.926412i | \(-0.377124\pi\) | ||||
0.376512 | + | 0.926412i | \(0.377124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42616.2 | 1.78543 | 0.892716 | − | 0.450620i | \(-0.148797\pi\) | ||||
0.892716 | + | 0.450620i | \(0.148797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4396.12 | 0.183513 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41612.2 | −1.73082 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16794.4 | 0.696043 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8253.60 | 0.340844 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9077.30 | −0.373520 | −0.186760 | − | 0.982406i | \(-0.559799\pi\) | ||||
−0.186760 | + | 0.982406i | \(0.559799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30545.6 | 1.25243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2539.66 | 0.103761 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15171.6 | 0.617654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25106.6 | −1.01851 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1570.84 | −0.0634997 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20953.2 | 0.844027 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18315.0 | −0.735163 | −0.367581 | − | 0.929991i | \(-0.619814\pi\) | ||||
−0.367581 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6080.09 | −0.243199 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13738.7 | −0.547615 | −0.273807 | − | 0.961785i | \(-0.588283\pi\) | ||||
−0.273807 | + | 0.961785i | \(0.588283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9424.20 | −0.374330 | −0.187165 | − | 0.982328i | \(-0.559930\pi\) | ||||
−0.187165 | + | 0.982328i | \(0.559930\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4974.82 | 0.196912 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40557.8 | 1.59977 | 0.799887 | − | 0.600151i | \(-0.204893\pi\) | ||||
0.799887 | + | 0.600151i | \(0.204893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16950.0 | −0.666263 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 229.191 | 0.00897778 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21869.2 | 0.853698 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47191.1 | −1.83583 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10317.9 | 0.400010 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −46135.2 | −1.78246 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12966.5 | −0.499258 | −0.249629 | − | 0.968342i | \(-0.580309\pi\) | ||||
−0.249629 | + | 0.968342i | \(0.580309\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2669.91 | 0.102450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15640.0 | −0.598098 | −0.299049 | − | 0.954238i | \(-0.596669\pi\) | ||||
−0.299049 | + | 0.954238i | \(0.596669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10326.2 | 0.393548 | 0.196774 | − | 0.980449i | \(-0.436953\pi\) | ||||
0.196774 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4024.65 | 0.152867 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2173.72 | 0.0822846 | 0.0411423 | − | 0.999153i | \(-0.486900\pi\) | ||||
0.0411423 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34651.3 | −1.30727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15260.2 | −0.573776 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1177.58 | −0.0441280 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3406.46 | 0.127224 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4978.10 | 0.185300 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46574.9 | 1.72787 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36051.4 | −1.33301 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2628.60 | −0.0968706 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7967.24 | −0.292641 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29981.6 | −1.09760 | −0.548800 | − | 0.835954i | \(-0.684915\pi\) | ||||
−0.548800 | + | 0.835954i | \(0.684915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29368.6 | 1.07161 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 725.040 | 0.0263684 | 0.0131842 | − | 0.999913i | \(-0.495803\pi\) | ||||
0.0131842 | + | 0.999913i | \(0.495803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15674.5 | 0.568183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3919.80 | 0.141623 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3167.54 | −0.114069 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1750.94 | 0.0628488 | 0.0314244 | − | 0.999506i | \(-0.489996\pi\) | ||||
0.0314244 | + | 0.999506i | \(0.489996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4922.39 | 0.176111 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41436.9 | −1.47769 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8219.48 | 0.292168 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23295.5 | −0.825376 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5500.62 | 0.194262 | 0.0971311 | − | 0.995272i | \(-0.469033\pi\) | ||||
0.0971311 | + | 0.995272i | \(0.469033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14447.5 | 0.508592 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7093.28 | −0.248900 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14881.3 | 0.520504 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55288.1 | −1.92762 | −0.963811 | − | 0.266586i | \(-0.914104\pi\) | ||||
−0.963811 | + | 0.266586i | \(0.914104\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3587.37 | 0.124675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47729.6 | 1.65350 | 0.826748 | − | 0.562573i | \(-0.190188\pi\) | ||||
0.826748 | + | 0.562573i | \(0.190188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21758.6 | −0.751388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11580.3 | −0.398631 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27191.6 | 0.933061 | 0.466530 | − | 0.884505i | \(-0.345504\pi\) | ||||
0.466530 | + | 0.884505i | \(0.345504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71076.5 | 2.43124 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3301.17 | −0.112563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2941.45 | 0.0999822 | 0.0499911 | − | 0.998750i | \(-0.484081\pi\) | ||||
0.0499911 | + | 0.998750i | \(0.484081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33718.3 | 1.14251 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4089.42 | 0.138132 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16494.5 | −0.555405 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9696.35 | 0.325479 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22191.3 | 0.742580 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42998.7 | −1.43438 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45733.8 | −1.52089 | −0.760445 | − | 0.649402i | \(-0.775019\pi\) | ||||
−0.760445 | + | 0.649402i | \(0.775019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1406.46 | −0.0466276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57658.9 | −1.90562 | −0.952812 | − | 0.303561i | \(-0.901824\pi\) | ||||
−0.952812 | + | 0.303561i | \(0.901824\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1268.74 | 0.0418025 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1952.80 | 0.0641431 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46156.4 | 1.51144 | 0.755718 | − | 0.654897i | \(-0.227288\pi\) | ||||
0.755718 | + | 0.654897i | \(0.227288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10126.5 | −0.330587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34869.1 | 1.13485 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10931.6 | −0.354694 | −0.177347 | − | 0.984148i | \(-0.556752\pi\) | ||||
−0.177347 | + | 0.984148i | \(0.556752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34026.3 | 1.10068 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1108.71 | −0.0357556 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11496.8 | 0.369644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15279.8 | 0.489788 | 0.244894 | − | 0.969550i | \(-0.421247\pi\) | ||||
0.244894 | + | 0.969550i | \(0.421247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2958.75 | 0.0945549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12518.6 | 0.398860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7648.81 | −0.242969 | −0.121485 | − | 0.992593i | \(-0.538766\pi\) | ||||
−0.121485 | + | 0.992593i | \(0.538766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8435.07 | 0.267141 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 752.4.a.c.1.2 | 3 | ||
4.3 | odd | 2 | 47.4.a.a.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 423.4.a.b.1.3 | 3 | |||
20.19 | odd | 2 | 1175.4.a.a.1.3 | 3 | |||
28.27 | even | 2 | 2303.4.a.a.1.1 | 3 | |||
188.187 | even | 2 | 2209.4.a.a.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
47.4.a.a.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
423.4.a.b.1.3 | 3 | 12.11 | even | 2 | |||
752.4.a.c.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1175.4.a.a.1.3 | 3 | 20.19 | odd | 2 | |||
2209.4.a.a.1.1 | 3 | 188.187 | even | 2 | |||
2303.4.a.a.1.1 | 3 | 28.27 | even | 2 |